OK,, not everyone is a math whiz.
But Isaac Newton (back in the late 17th century) was certainly both great scientist and great mathematician.  He worked out the whole science of “mechanics,” i.e. how things move!
And he developed a whole new kind of math to help describe the business of objects in motion (calculus).

It turns out that it doesn’t require calculus to do some great stuff with the LAW OF GRAVITY…. which just says that the FORCE of gravity, is directly related to the masses of objects in question, and the distance between them.  Perhaps you’ve seen the equation,  F=GmM/r²,
In this equation,  m can be the mass of an object falling towards earth’s surface, and M is the mass of the earth.
G is a constant that was determined in the 18th century (courtesy of a rather eccentric wealthy English scientist, Henry Cavendish) and  r is the radius of earth.

Once G was worked out by Mr. Cavendish, and since we know the acceleration of objects at earth’s surface,, about 10m per second squared, it’s possible to evaluate the mass of the earth!
It’s about 6×10²⁴ kilograms (6 followed by 24 zeros).
That’s a lot of kilograms!

OK, now here is the cool part— if you know the mass of the earth, and you know the size of the earth (which provides us the volume),
THEN it’s easy to get the density–  remember?– density is just mass divided by volume.

The earth’s AVERAGE density works out to about 5.5 g/cm³  (0r 5500 kg/m³)…
And,
This is kind of weird, because rocks have average denisty of around 2.5 or 2.6 g/cm³ ….. SO, this suggests that there is something really dense deep in the earth, which bumps up the average density of our planet.
What could it be?
Well, at this point, you probably know– the metallic Fe-rich core!  (which has a density of around 8 g/cm³)

Anyway, watch the video if you like,, and fast forward through it, if math just isn’t your thing!
(You will not be tested on your ability reproduce the math.)

Last but NOT LEAST, WHY LAYERS?

In science, some of the best questions are the most obvious ones!
Ever since elementary school science classes, we’ve learned that our planet has layers.
Why?

First off, the layers are concentric spheres.
The layers might be based on physical properties like liquid/solid, brittle/ductile, and hence describing things like inner/outer core and lithosphere/asthenosphere; or they might be based on chemical composition like felsic/mafic, rocky/metallic, and hence describing things like  crust/mantle, or core/mantle.
But no matter what, the layers are basically concentric spheres.  This is undoubtedly due to gravity.  Objects with enough mass tend to pull themselves into spherical shape.  Admittedly, things like planets and stars are not perfectly spherical, but they are pretty close.  Lower mass objects like asteroids are rarely spherical, as there is just not enough mass to gravitational generate sphericity.

The second aspect is trickier– why layers at all?
Did the earth form in layers, with an iron core serving as a starting point to which rocky material was added, rolling-snow-ball-style?
Or did the earth initially form as a homogeneous mass and later “differentiate” into its current heterogeneous layered form?
In general, scientists believe that the latter is most likely the case.
In fact, one of the key features of our models for planet formation (particularly the rocky inner “terrestrial” planets) is that the process of formation results in very high temperatures.
Young planets are particularly “hot” because:

1. Heat from accretion.  Lots of pieces of space junk slamming in to each other and sticking together but also transforming kinetic energy into heat.
2. Heat from gravitational pressure.  So much material, condensing and squeezing together, releases heat.
3. Heat from radioactive decay.  Later we’ll learn a bit about radioactivity and its usage in determining rock ages, but radioactive elements are simply present in rocky “terrestrial” worlds and the associated radioactive decay releases heat.

As the proto-earth heated up, melting of material took place, and the denser material sank towards the core.  This is why iron (a relatively dense metal) makes up our core.  This is also why crustal rocks are enriched in somewhat lower density material like silica, aluminum, and potassium.

Here is a good (short and sweet) synopsis, via fun video, from Public Broadcasting, PBS– and, I might add, pretty spot on!  Check it out,